Question

Express the area of an equilateral triangle as a function of the length of a side.

Short answer

The expression for the area of the equilateral triangle as a function of length is \({\bf{A}}\left( {\bf{L}} \right){\bf{ = }}\frac{{\sqrt {\bf{3}} }}{{\bf{4}}}{{\bf{L}}^{\bf{2}}}\) and domain of the function is\(\left( {{\bf{0,}}\infty } \right)\).

Step-by-step solution

Determine the equation for the area of the equilateral triangle

Let the length of a side of an equilateral triangle be L, then its area is given as;

\(A\left( L \right) = \frac{{\sqrt 3 }}{4}{L^2}\)

Here, \(L\)is the length equilateral triangle, \(A\) is the area of the equilateral triangle.

Determine the domain for the area of the equilateral triangle

The area of the equilateral triangle is true for all positive values of its sides, so the domain of the equilateral triangle is given as:

\(0 < L < \infty \)

The domain for the area of the equilateral triangle as a function length is\(\left( {0,\infty } \right)\)

Therefore, the expression for the area of the equilateral triangle as a function of length is \(A\left( L \right) = \frac{{\sqrt 3 }}{4}{L^2}\) and domain of the function is\(\left( {0,\infty } \right)\).